发帖
雷达卡
摘要翻译：
本文研究了Max-Plus代数中的一种新的上鞅分解，其实质是将$(\mathcal{D}）类的任何上鞅表示为某个运行的上确界过程的条件期望。作为一个应用，我们展示了极大正上鞅分解是如何在不计算期权价格的情况下解决美式最优停止问题的。然后给出了一些基于一维扩散过程的示例。另一个有趣的应用涉及投资组合保险。因此，本文基于“极大鞅”，解决了一个优化问题，其目标是在给定的地板过程中（在每个中间日期）找到最优鞅。终端值上的凸序。
---
英文标题：
《Max-Plus decomposition of supermartingales and convex order. Application
to American options and portfolio insurance》
---
作者：
Nicole El Karoui, Asma Meziou
---
最新提交年份：
2008
---
分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
--
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--
---
英文摘要：
We are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class $(\mathcal{D})$ as a conditional expectation of some running supremum process. As an application, we show how the Max-Plus supermartingale decomposition allows, in particular, to solve the American optimal stopping problem without having to compute the option price. Some illustrative examples based on one-dimensional diffusion processes are then provided. Another interesting application concerns the portfolio insurance. Hence, based on the ``Max-Plus martingale,'' we solve in the paper an optimization problem whose aim is to find the best martingale dominating a given floor process (on every intermediate date), w.r.t. the convex order on terminal values.
---
PDF链接：
https://arxiv.org/pdf/0804.2561
提升卡
置顶卡
沉默卡
变色卡
抢沙发
千斤顶
显身卡
京公网安备 11010802022788号
